Re: fft of exponential function and normalization

On Fri, 25 Jul 2014 02:35:18 +0000 (UTC), "Daniel kiracofe"
<daniel.kiracofe@gmail.nospam> wrote:

> this is a commonly confused point. There are 4 thing that we associate Mr. Fourier's name with: Fourier transform, Fourier series, Discrete Time Fourier Transform, and Discrete Fourier transform. The FFT is a special case of the Discrete Fourier Transform. This is NOT the same thing as a Fourier transform. You are comparing apples and oranges. Matlab cannot do a Fourier transform, only a discrete fourier transform. If you really want a Fourier transform, use a computer algebra system like Maple or Mathematica.
>
>Daniel
>

While this is strictly correct, it is clear that the theorectial and
calcuated results show the same general behaviour. So, how
to 'line them up'?

I would suggest some reading. There are lots of sources that
will give you the link between the Fourier Transform and the DFT
coefficients -- yes, it is a matter of normalisation and getting
the units right. You will see that the sampling frequency of
the DFT is involved in the connection.

This is a general problem when one tries to compare a
continuous quantity with a discrete analog. Would also
suggest that you look into how connets a probability
density function and a histogram. Same issues!

CR